Problem: Rewrite as a simplified fraction. ${3.4\overline{70} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3470.707...\\ 10x &= 34.707...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3436}$ ${x = \dfrac{3436}{990}} $ ${x = \dfrac{1718}{495}} \text{or} {3 \dfrac{233}{495}}$